Non-perturbative BRST symmetry and the spectral structure of the ghost propagator

On the base of experimental data it was revealed that type of wave breaking depends on wave asymmetry against the vertical axis at wave breaking point. The asymmetry of waves is defined by spectral structure of waves: by the ratio between amplitudes of first and second nonlinear harmonics and by phase shift between them. The relative position of nonlinear harmonics is defined by a stage of nonlinear wave transformation and the direction of energy transfer between the first and second harmonics. The value of amplitude of the second nonlinear harmonic in comparing with first harmonic is significantly more in waves, breaking by spilling type, than in waves breaking by plunging type. The waves, breaking by plunging type, have the crest of second harmonic shifted forward to one of the first harmonic, so the waves have "saw-tooth" shape asymmetrical to vertical axis. In the waves, breaking by spilling type, the crests of harmonic coincides and these waves are symmetric against the vertical axis. It was found that limit height of breaking waves in empirical criteria depends on type of wave breaking, spectral peak period and a relation between wave energy of main and second nonlinear wave harmonics. It also depends on surf similarity parameter defining conditions of nonlinear wave transformations above inclined bottom.

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Geometry and Quantum Dynamics

10.1093/oso/9780198788393.003.0014 ◽

2017 ◽

Author(s):

Laurent Baulieu ◽

John Iliopoulos ◽

Roland Sénéor

Keyword(s):

General Relativity ◽

Quantum Dynamics ◽

Gauge Theories ◽

Brst Symmetry ◽

Abelian Gauge ◽

Yang Mills ◽

History Of ◽

Brst Invariance

A geometrical derivation of Abelian and non- Abelian gauge theories. The Faddeev–Popov quantisation. BRST invariance and ghost fields. General discussion of BRST symmetry. Application to Yang–Mills theories and general relativity. A brief history of gauge theories.

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Thermodynamic Green’s Functions and Spectral Structure

10.1093/oso/9780198791942.003.0007 ◽

2018 ◽

Author(s):

Norman J. Morgenstern Horing

Keyword(s):

Green’S Function ◽

Green's Function ◽

Green's Functions ◽

Green’S Functions ◽

Spectral Weight ◽

Statistical Thermodynamic ◽

Spectral Structure ◽

Imaginary Time ◽

Translational Invariance ◽

The One

Multiparticle thermodynamic Green’s functions, defined in terms of grand canonical ensemble averages of time-ordered products of creation and annihilation operators, are interpreted as tracing the amplitude for time-developing correlated interacting particle motions taking place in the background of a thermal ensemble. Under equilibrium conditions, time-translational invariance permits the one-particle thermal Green’s function to be represented in terms of a single frequency, leading to a Lehmann spectral representation whose frequency poles describe the energy spectrum. This Green’s function has finite values for both t>t′ and t<t′ (unlike retarded Green’s functions), and the two parts G1> and G1< (respectively) obey a simple proportionality relation that facilitates the introduction of a spectral weight function: It is also interpreted in terms of a periodicity/antiperiodicity property of a modified Green’s function in imaginary time capable of a Fourier series representation with imaginary (Matsubara) frequencies. The analytic continuation from imaginary time to real time is discussed, as are related commutator/anticommutator functions, also retarded/advanced Green’s functions, and the spectral weight sum rule is derived. Statistical thermodynamic information is shown to be embedded in physical features of the one- and two-particle thermodynamic Green’s functions.

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Gauge Field Theory in Natural Geometric Language

10.1093/oso/9780198861492.001.0001 ◽

2020 ◽

Author(s):

Daniel Canarutto

Keyword(s):

Particle Physics ◽

Quantum Physics ◽

Brst Symmetry ◽

Natural Extension ◽

Integrated Approach ◽

Arbitrary Spin ◽

Field Theories ◽

Quantum Field Theories ◽

Standard View ◽

Spinor Bundle

This monograph addresses the need to clarify basic mathematical concepts at the crossroad between gravitation and quantum physics. Selected mathematical and theoretical topics are exposed within a not-too-short, integrated approach that exploits standard and non-standard notions in natural geometric language. The role of structure groups can be regarded as secondary even in the treatment of the gauge fields themselves. Two-spinors yield a partly original ‘minimal geometric data’ approach to Einstein-Cartan-Maxwell-Dirac fields. The gravitational field is jointly represented by a spinor connection and by a soldering form (a ‘tetrad’) valued in a vector bundle naturally constructed from the assumed 2-spinor bundle. We give a presentation of electroweak theory that dispenses with group-related notions, and we introduce a non-standard, natural extension of it. Also within the 2-spinor approach we present: a non-standard view of gauge freedom; a first-order Lagrangian theory of fields with arbitrary spin; an original treatment of Lie derivatives of spinors and spinor connections. Furthermore we introduce an original formulation of Lagrangian field theories based on covariant differentials, which works in the classical and quantum field theories alike and simplifies calculations. We offer a precise mathematical approach to quantum bundles and quantum fields, including ghosts, BRST symmetry and anti-fields, treating the geometry of quantum bundles and their jet prolongations in terms Frölicher's notion of smoothness. We propose an approach to quantum particle physics based on the notion of detector, and illustrate the basic scattering computations in that context.

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Data Augmentation and Spectral Structure Features for Limited Samples Hyperspectral Classification

Remote Sensing ◽

10.3390/rs13040547 ◽

2021 ◽

Vol 13 (4) ◽

pp. 547

Author(s):

Wenning Wang ◽

Xuebin Liu ◽

Xuanqin Mou

Keyword(s):

Classification Accuracy ◽

Data Augmentation ◽

Classification Problem ◽

Classification Performance ◽

Spectral Structure ◽

Limited Sample ◽

Sample Classification ◽

Training Samples ◽

Traditional Classification ◽

Hyperspectral Classification

For both traditional classification and current popular deep learning methods, the limited sample classification problem is very challenging, and the lack of samples is an important factor affecting the classification performance. Our work includes two aspects. First, the unsupervised data augmentation for all hyperspectral samples not only improves the classification accuracy greatly with the newly added training samples, but also further improves the classification accuracy of the classifier by optimizing the augmented test samples. Second, an effective spectral structure extraction method is designed, and the effective spectral structure features have a better classification accuracy than the true spectral features.

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Extended High Frequencies Provide Both Spectral and Temporal Information to Improve Speech-in-Speech Recognition

Trends in Hearing ◽

10.1177/2331216520980299 ◽

2020 ◽

Vol 24 ◽

pp. 233121652098029

Author(s):

Allison Trine ◽

Brian B. Monson

Keyword(s):

Speech Recognition ◽

Pure Tone ◽

Recognition Performance ◽

Low Frequency ◽

Exploratory Analysis ◽

Temporal Information ◽

Significant Benefit ◽

Head Orientation ◽

Spectral Structure ◽

High Frequencies

Several studies have demonstrated that extended high frequencies (EHFs; >8 kHz) in speech are not only audible but also have some utility for speech recognition, including for speech-in-speech recognition when maskers are facing away from the listener. However, the contribution of EHF spectral versus temporal information to speech recognition is unknown. Here, we show that access to EHF temporal information improved speech-in-speech recognition relative to speech bandlimited at 8 kHz but that additional access to EHF spectral detail provided an additional small but significant benefit. Results suggest that both EHF spectral structure and the temporal envelope contribute to the observed EHF benefit. Speech recognition performance was quite sensitive to masker head orientation, with a rotation of only 15° providing a highly significant benefit. An exploratory analysis indicated that pure-tone thresholds at EHFs are better predictors of speech recognition performance than low-frequency pure-tone thresholds.

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